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Can you explain the difference between these two sentences?

I cannot go to school.
I can not go to school.

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  • There are three different animals: can't, cannot, can not. There are some uses common to them (to all three, or to just two). There are some uses that aren't common. All three animals are found in today's standard English, and are acceptable.
    – F.E.
    Oct 23, 2014 at 1:40
  • Interestingly, a similar thread has just shown up recently over in ELU land: english.stackexchange.com/questions/204006/…
    – F.E.
    Oct 23, 2014 at 1:44

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I cannot go to school

  • This would mean that, for whatever reason (e.g. ill health), you were unable to attend school due to circumstances outside your control.

I can not go to school

  • Your girlfriend just got a day off and wants to hang with you. It is well within your abilities to NOT go to school.. you are making a decision to purposefully avoid it.
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    Cannot and can not are alternative spellings of the same word. One can just as well emphasize the not in the first spelling by pronouncing the word as cannot.
    – user6951
    Oct 22, 2014 at 20:54
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    "I can not go to school" could have either meaning, depending on whether not is interpreted as negating can (in which case it's synonymous with cannot/can't) or as negating go to school. If the latter is intended, it's a mistake to write it as one word.
    – user230
    Oct 22, 2014 at 23:59
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In British English, the accept negative form of 'can' is cannot (one word). I cannot (often contracted to I can't especially in speech) go to school almost certainly means I am unable to got to school / It is not possible for me to go to school. It could also mean I may not (= am not allowed to) go to school, though this would need to be made clear by the context.

The 'ability/possibility' meaning is shown in:

I cannot (can't) go to school) because we are snowed in.

The 'permission' meaning is shown in:

My father says I cannot (can't) go to school. He says that education is only for boys.

I can not go to school is more problematic. It could be that the person who wrote this has simply not written the two words as one. This is a very common 'mistake', because 'not' is not written together with the verb that precedes it with any other verb. Indeed, some people would not consider this to be a mistake. Note that we cannot tell in speech the difference between 'can not' and 'cannot'. Both forms can be contracted to 'can't'.

A second, less common, possibility for 'can not' is that it means 'have the ability not to'. In this sense, the two words are always written separately. In speech,, there is a slight but discernible pause between them, and the 'not' is stressed. An example of this is:

A: You have to go to school tomorrow. You can't not go.

B: I can not go. Nobody can make me.

Note that, as we see from A's words, this form can have a 'double negative; You can't not go (It is not possible/permissible for you not to go) does not mean the same as You can go.

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They are interchangeable, although "cannot" is the more common and preferred spelling. "Can not" can be used for emphasis as in:

No, I can not go to school.

or when it is followed by another construction:

I can not only walk, I can also run.

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